By Khalid Abidi, Jian-Xin Xu
This publication covers a large spectrum of platforms resembling linear and nonlinear multivariable structures in addition to keep watch over difficulties equivalent to disturbance, uncertainty and time-delays. the aim of this publication is to supply researchers and practitioners a handbook for the layout and alertness of complicated discrete-time controllers. The ebook provides six diversified regulate ways looking on the kind of process and keep watch over challenge. the 1st and moment techniques are according to Sliding Mode keep watch over (SMC) concept and are meant for linear platforms with exogenous disturbances. The 3rd and fourth techniques are in response to adaptive regulate concept and are geared toward linear/nonlinear platforms with periodically various parametric uncertainty or structures with enter hold up. The 5th technique is predicated on Iterative studying keep watch over (ILC) thought and is geared toward doubtful linear/nonlinear structures with repeatable initiatives and the ultimate method relies on fuzzy good judgment keep watch over (FLC) and is meant for hugely doubtful platforms with heuristic keep an eye on wisdom. distinctive numerical examples are supplied in each one bankruptcy to demonstrate the layout technique for every keep watch over approach. a couple of functional keep watch over functions also are provided to teach the matter fixing approach and effectiveness with the complex discrete-time keep an eye on ways brought during this book.
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Extra info for Advanced Discrete-Time Control: Designs and Applications
140) is based the current value of the disturbance d1,k which is unknown and therefore cannot be implemented in this current form. 141) therefore, the final controller structure is given by u k = (sγ )−1 srk+1 − sΦrk + sΦek + βek − (sγ )−1 sdˆ k . 7 with regard to the closed-loop stability, first derive the closed-loop error dynamics. 139), we obtain ek+1 = Φ − γ (sγ )−1 sΦ ek − β (sγ )−1 ek − dk p + γ (sγ )−1 sdˆ k + I − γ (sγ )−1 s (rk+1 − Φrk ) . 143), we note that since the objective is to have xk → rk then there must exist a control input u m,k such that rk+1 = Φrk + γ u m,k .
123). 4 allowing a fast enough convergence. From Fig. 10 the estimation of error x˜2,k is plotted. 3 Fig. 4 Fig. 11 Disturbance η and estimate ηˆ and deviating only when the discontinuities occur but attenuates very quickly. The disturbance estimation is seen in Fig. 11 and the estimation converges quickly to the actual disturbance. From Fig. 12 we can see the tracking error performance. The tracking error is about 6 × 10−6 which matches the theoretical results of O T 2 bound. Again like the previous two approaches, the control signal of the ISM control is smaller than that of the PI controller at the initial phase (Fig.
4 t [sec] Fig. 05 Fig. 3 t [sec] Fig. 25 t [sec] Fig. 5 Discrete-Time Terminal Sliding Mode Control In this section we will discuss the design of the tracking controller for the system. The controller will be designed based on an appropriate sliding surface. Further, the stability conditions of the closed-loop system will be analyzed. The relation between TSM control properties and the closed-loop eigenvalue will be explored. Note that the subsequent analysis and derivations will be based on a 2nd order system example, however, it is possible to apply the same principles for a system of higher order as long as it is SISO.
Advanced Discrete-Time Control: Designs and Applications by Khalid Abidi, Jian-Xin Xu